Controllers for regulated power inverters, AC/DC, and DC/DC converters

ABSTRACT

The present invention relates to methods and corresponding apparatus for regulated and efficient DC-to-AC conversion with power quality, and to methods and corresponding apparatus for regulation and control of said DC-to-AC conversion. The invention further relates to methods and corresponding apparatus for regulation and control of AC-to-DC and/or DC-to-DC conversion.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 15/646,692, filed 11 Jul. 2017. This application also claimsthe benefit of the U.S. provisional patent applications 62/362,764 filedon 15 Jul. 2016, and 62/510,990 filed on 25 May 2017.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

None.

COPYRIGHT NOTIFICATION

Portions of this patent application contain materials that are subjectto copyright protection. The copyright owner has no objection to thefacsimile reproduction by anyone of the patent document or the patentdisclosure, as it appears in the Patent and Trademark Office patent fileor records, but otherwise reserves all copyright rights whatsoever.

TECHNICAL FIELD

The present invention relates to methods and corresponding apparatus forregulated and efficient DC-to-AC conversion with high power quality, andto methods and corresponding apparatus for regulation and control ofsaid DC-to-AC conversion. The invention further relates to methods andcorresponding apparatus for regulation and control of AC-to-DC and/orDC-to-DC conversion.

BACKGROUND

A power inverter, or an inverter, or a DC-to-AC converter, is anelectronic device or circuitry that changes direct current (DC) toalternating current (AC) (e.g. single- and/or 3-phase).

A power inverter would typically be a switching inverter that uses aswitching device (solid-state or mechanical) to change DC to AC. Thereare may be many different power circuit topologies and controlstrategies used in inverter designs. Different design approaches addressvarious issues that may be more or less important depending on the waythat the inverter is intended to be used. For example, an inverter mayuse an H bridge that is built with four switches (solid-state ormechanical), that enables a voltage to be applied across a load ineither direction.

Given a particular power circuit topology, an appropriate controlstrategy may need to be chosen in order to meet the desired inverterspecifications, e.g. in terms of input and output voltages, AC andswitching frequencies, output power and power density, power quality,efficiency, cost, and so on.

For example, one of the most obvious approaches to increase powerdensity would be to increase the frequency that the inverter operates at(“switching frequency”). This may be done by employing wide-bandgap(WBG) semiconductors that use materials such as gallium nitride (GaN) orsilicon carbide (SiC) and can function at higher power loads andfrequencies, allowing for smaller, more energy-efficient devices.

A typical way to control a switching inverter is by mathematicallydefining voltage and/or current relations at different switching statesto produce the “desired” output, obtaining the appropriate digitallysampled voltage and/or current values, then using numerical signalprocessing tools to implement an appropriate algorithm to control theswitches [1]. However, such a straightforward approach often calls forperformance compromises based on the ability to accurately define thevoltage and current relations for various topological stages and loadconditions (e.g. nonlinear loads), and to account for nonidealities andtime variances of the components (since the values of, e.g.,resistances, capacitances, inductances, switches' behavior etc., maychange in time due to the temperature changes, mechanicalstress/vibrations, aging, etc.). In addition, a control processor forthe inverter must meet a number of real-time processing challenges,especially at high switching frequencies, in order to effectivelyexecute the algorithms required for efficient DC/AC conversion andcircuit protection. Various design and implementation compromises areoften made in order to overcome these challenges, and those cannegatively impact the complexity, reliability, cost, and performance ofthe inverter.

Thus there is a need in a simple analog (i.e. continuous and real-time)controller that would allow us to bypass the detailed analysis ofvarious topological stages during a switch ng cycle altogether, thusavoiding the pitfalls and limitations of straightforward digitaltechniques.

Further, there is a need in such a simple controller that (i) does notrequire any current sensors, or additional start-up and managementmeans, (ii) provides robust, high quality (e.g. low voltage and currentharmonic distortions), and well regulated AC outputs for a wide range ofpower factor loads, including highly nonlinear loads, and also (iii)offers multiple ways to optimize the cost-size-weight-performancetradespace.

SUMMARY

The present invention overcomes the limitations of the prior art byintroducing an Inductor Current Mapping, or ICM controller. The ICMcontroller offers various overall advantages over respective digitalcontrollers, and may provide multiple ways to optimize thecost-size-weight-performance tradespace.

In the detailed description that follows, we first introduce anidealized concept of an analog ICM controller for an H-bridge powerinverter. We show how the “actual” voltage-current relations in thefilter inductors may be directly “mapped,” by the constraints imposed bytwo Schmitt triggers, to the voltage relations among the inputs and theoutput of the controller's analog integrator, providing the desiredinverter output that effectively proportional to the reference voltage.We then discuss the basic operation and properties of this inverter andits associated ICM controller, using particular implementations forillustration. Further, we describe a simple controller modification thatmay improve the transient responses by utilizing a feedback signalproportional to the load current. Next, we discuss extensions of the ICMconcept to other hard- or soft-switching power inverters (e.g. for3-phase inverters), and for AC/DC and DC/DC converter topologies, andthe use of ICM controllers in DC/DC converters for voltage, current, andpower regulation.

Further scope and the applicability of the invention will be clarifiedthrough the detailed description given hereinafter. It should beunderstood, however, that the specific examples, while indicatingpreferred embodiments of the invention, are presented for illustrationonly. Various changes and modifications within the spirit and scope ofthe invention should become apparent to those skilled in the art fromthis detailed description. Furthermore, all the mathematicalexpressions, diagrams, and the examples of hardware implementations areused only as a descriptive language to convey the inventive ideasclearly, and are not limitative of the claimed invention.

BRIEF DESCRIPTION OF FIGURES

FIG. 1. Basic diagram of an asynchronous buck inverter of the presentinvention and its associated controller.

FIG. 2. Alternative grounding configuration of the inverter and itsassociated controller shown in FIG. 1.

FIG. 3. Illustrative steady-state voltage and current waveforms for theinverter and its associated controller shown in FIGS. 1 and 2. Low FCSfrequency (6 kHz) is used for better waveform visibility.

FIG. 4. Illustrative transient voltage and current waveforms for theinverter and its associated controller shown in FIGS. 1 and 2. Low FCSfrequency (6 kHz) is used for better waveform visibility.

FIG. 5. Illustrative schematic of a controller circuit implementation.

FIG. 6. Illustrative schematic of a particular implementation of theinverter and its associated controller shown in FIG. 1.

FIG. 7. Simulated MOSFET and total power losses, efficiency, and totalharmonic distortions as functions of the output power for the particularinverter implementation shown in FIG. 6 (48 kHz FCS, resistive load).

FIG. 8. Illustrative steady-state voltage and current waveforms for alagging PF=0.5 load (66.2 mH inductor in series with 14.4 Ω resistor),for the inverter and its associated controller shown in FIG. 6 (48 kHzFCS).

FIG. 9. Illustrative transient voltage and current waveforms for alagging PF load (50 mH inductor in series with 10.8 Ω or 84.4 Ωresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 10. Illustrative steady-state voltage and current waveforms for aleading PF=0.5 load (106 μF capacitor in series with 14.4 Ω resistor),for the inverter and its associated controller shown in FIG. 6 (48 kHzFCS).

FIG. 11. Illustrative transient voltage and current waveforms for aleading PF load (70.7 μF capacitor in series with 21.6 Ω or 1 MΩresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 12. Illustrative schematic of a particular implementation of afree-running version of the inverter and its associated controller shownin FIG. 1.

FIG. 13. Power spectra of the common and differential mode outputvoltages for the particular FCS-based (FIG. 6) and free-running (FIG.12) implementations. The vertical dashed lines are at 150 kHz.

FIG. 14. An H-bridge inverter with a free-running ICM controller.

FIG. 15. Example of full-range transient waveforms for ohmic load.

FIG. 16. Transient waveforms for nonlinear (full-wave diode rectifier)load (2 kW).

FIG. 17. Transient waveforms for changes in V_(ref) (“instantaneous”synchronization with reference).

FIG. 18. Illustrative steady state waveforms at full (2 kW) resistiveload.

FIG. 19. Illustrative steady state waveforms at 10% (200 W) resistiveload.

FIG. 20. Full-load (2 kW) waveforms on 2.8 ms to 3 ms interval.

FIG. 21. 10%-load (200 W) waveforms on 2.8 ms to 3 ms interval.

FIG. 22. PSD of inductor current at full and 10% loads.

FIG. 23. Efficiency and THD as functions of output power.

FIG. 24. Illustrative startup voltages and currents.

FIG. 25. Inverter and ICM controller with load current feedback.

FIG. 26. Transient responses for leading PF=0.5 load without (left) andwith (right) current feedback.

FIG. 27. Buck-boost DC/DC converter with ICM controller.

FIG. 28. Example of transient waveforms for the converter shown in FIG.27 configured for voltage, current, and power regulation.

FIG. 29. Startup voltages and currents for the buck-boost DC/DCconverter with ICM controller.

FIG. 30. Illustrative example of an ICM-controlled 3-phase inverter.

FIG. 31. Example of full-range transient waveforms for theICM-controlled 3-phase inverter shown in FIG. 30.

FIG. 32. Startup voltages and currents when the 3 kW ICM-control 3-phaseinverter shown in FIG. 30 is connected to a low (p.f.=0.1) lagging powerfactor load in Δ configuration, with the apparent power of about 3 kW.

FIG. 33. Example of a single-phase H-bridge ICM-based AC/DC converterwith high power factor and low harmonic distortions.

FIG. 34. Illustration of the behavior of a particular implementation ofa 2 kW ICM-controlled single-phase AC/DC converter shown in FIG. 33.

FIG. 35. Illustration of variations in ICM controller topologies.

FIG. 36. Example of a 3-phase ICM-based AC/DC converter with high powerfactor and low harmonic distortions.

FIG. 37. Illustration of the behavior of a particular implementation ofa 6 kW ICM-controlled 3-phase AC/DC converter shown in FIG. 36.

FIG. 38. PSDs of line currents and V_(CM)-V_(N) for a particularimplementation of a 6 kW ICM-controlled 3-phase AC/DC converter shown inFIG. 36.

FIG. 39. Example of ICM-based control of a 3-phase AC/DC converter thatis effectively equivalent to that shown in FIG. 36.

FIG. 40. Illustrative example of using the 3-phase AC/DC convertersshown in FIG. 36 and FIG. 39 for 3-phase DC/AC conversion.

FIG. 41. Illustration of transient output power, voltages and currents,and the inductor currents, for a particular implementation of a 6 kWICM-controlled 3-phase inverter shown in FIG. 40, in response tofull-range (and independent of each other) step changes in theline-to-line resistive loads.

ABBREVIATIONS

AC: alternating (current or voltage);

BCM: Boundary Conduction Mode; BOM: Bill Of Materials;

CCM: Continuous Conduction Mode; CM: Common Mode; COTS: CommercialOff-The-Shelf;

DC: direct (current or voltage), or constant polarity (current orvoltage); DCM: Discontinuous Conduction Mode; DCR: DC Resistance of aninductor; DM: Differential Mode; DSP: Digital SignalProcessing/Processor;

EMC: electromagnetic compatibility; e.m.f.: electromotive force; EMI:electromagnetic interference; ESR: Equivalent Series Resistance;

FCS: Frequency Control Signal;

GaN: Gallium nitride;

ICM: Inductor Current Mapping; IGBT: Insulated-Gate Bipolar Transistor;

MATLAB: MATrix LABoratory (numerical computing environment andfourth-generation programming language developed by MathWorks); MOS:Metal-Oxide-Semiconductor; MOSFET: Metal Oxide SemiconductorField-Effect Transistor; MTBF: Mean Time Between Failures;

NDL: Nonlinear Differential Limiter;

PF: Power Factor; PFC: Power Factor Correction; PoL: Point-of-Load; PSD:Power Spectral Density; PSM: Power Save Mode; PWM: Pulse-WidthModulator;

RFI: Radio Frequency Interference; RMS: Root Mean Square;

SCS: Switch Control Signal; SiC: Silicon carbide; SMPS: Switched-ModePower Supply; SMVF: Switched-Mode Voltage Follower; SMVM: Switched-ModeVoltage Mirror; SNR: Signal to Noise Ratio; SCC: Switch Control Circuit;

THD: Total Harmonic Distortion;

UAV: Unmanned Aerial Vehicle; ULISR: Ultra Linear Isolated SwitchingRectifier; ULSR(U): Ultra Linear Switching Rectifier (Unit);

VN: Virtual Neutral; VRM: Voltage Regulator Module;

WBG: wide-bandgap;

ZVS: Zero Voltage Switching; ZVT: Zero Voltage Transition;

DETAILED DESCRIPTION 1. Illustrative Description of an Asynchronous BuckInverter of the Present Invention and of its Principles of Operation

Let us first consider the simplified circuit diagram shown in FIG. 1.

This power inverter would be capable of converting the DC source voltageinto the AC output voltage V_(out) that is indicative of the ACreference voltage V_(ref).

In FIG. 1, the DC source voltage V_(in) is shown to be provided by abattery, and the resistor connected in series with the battery indicatesthe battery's internal resistance.

Capacitance of the capacitor connected in parallel to the battery wouldneed to be sufficiently large (for example, of order 10 μF) to provide arelatively low impedance path for high-frequency current components. Asignificantly larger capacitance may be used (e.g., of order 1 mF,depending on the battery's internal resistance) to reduce the lowfrequency (e.g., twice the AC frequency) input current and voltageripples.

In FIG. 1, the DC source voltage V_(in) is shown to be applied to theinput of the H bridge comprising two pairs of switches (labeled “1” and“2”), and the output voltage of the H bridge is the switching voltageV*. For example, when the switches of the 2nd pair are “on” and theswitches of the 1st pair are “off”, V* would be effectively equal toV_(in), and when the switches of the 1st pair are “on” and the switchesof the 2nd pair are “off”, V* would be effectively equal to −V_(in).

The diodes explicitly shown in FIG. 1 as connected across the switchesin the bridge would enable a non-zero current through the inductors whenall switches in the bridge are “off”. All switches the bridge being“off” may be viewed as asynchronous state of the inverter. During theasynchronous state, and depending on the magnitude and the direction ofthe current through the inductors, the switching voltage V* may havevalues between −V_(in) and V_(in).

One skilled in the art will recognize that, for example, if the switchesare implemented using power MOSFETs, the diodes explicitly shown in FIG.1 may be the MOSFET body diodes.

The switching voltage V* is further filtered with an LC filteringnetwork to produce the output voltage V_(out). In FIG. 1, this networkperforms both differential mode (DM) filtering to produce the outputdifferential voltage V_(out), and common mode (CM) filtering to reduceelectromagnetic interference (EMI). The DM filtering bandwidth of the LCnetwork should be sufficiently narrow to suppress the switchingfrequency and its harmonics, while remaining sufficiently larger thanthe AC frequency.

The DM inductance L in FIG. 1 may be provided by physical inductors, byleakage inductance of the CM choke, or by combination thereof.

The switches of the 1st and 2nd pairs in the bridge are turned “on” or“off” by the respective switch control signals (SCSs), labeled as Q₁ andQ₂, respectively, in FIG. 1. In the figure, it is implied that theswitches are turned “on” by a high value of the respective SCS, and areturned “off” by the low value of the SCS.

In FIG. 1, the input to the integrator (with the integration timeconstant T) is a sum of the AC reference voltage V_(ref) and a voltageproportional to the switching voltage, μV*, and the output of theintegrator contributes to the inputs of both inverting and non-invertingcomparators. The comparators may also be characterized by sufficientlylarge hysteresis, e.g., be configured as Schmitt triggers.

When the comparators are configured as Schmitt triggers, the frequencycontrol signal (FCS) V_(FCS) may be optional, as would be discussedfurther in the disclosure. Such a configuration of the inverter (withoutan FCS) would be a free-running configuration.

A (constant) positive threshold offset, or FCS offset, signal ΔV_(FCS)is added to the input of the non-inverting comparator in FIG. 1. Thisoffset signal enables the SCSs Q₁ and Q₂ to simultaneously have lowvalues, thus keeping all switches in the bridge “off”, and thus enablingan asynchronous state of the inverter.

A periodic FCS V_(FCS) may be added to the inputs of both inverting andnon-inverting comparators to enable switching at typically constant(rather than variable) frequency, effectively equal to the FCSfrequency.

A signal proportional to the output AC voltage, μT/T V_(out), is addedto the inputs of both inverting and non-inverting comparators fordamping transient, responses of the inverter caused by changes in theload (load current). The mechanism of such damping, and the choice ofthe time parameter τ, would be discussed further in the disclosure. Oneskilled in the art will recognize that, equivalently, a signalproportional to the time derivative of the output AC voltage, μτ{dotover (V)}_(out), may be added to the input of the integrator.

It may be important to point out that the output AC voltage V_(out) ofthe inverter of the present invention would be effectively independentof the DC source voltage V_(in), as long as (neglecting the voltagedrops across the switches and the inductors) |V_(in)| is larger than|V_(out)|.

The grounding configuration of the inverter shown in FIG. 1 would beappropriate for the 240 V split phase configuration, similar to whatwould be found in North American households.

FIG. 2 shows the modification of the inverter appropriate for the 240V-to-ground configuration, similar to what would be found in Europeanand other households around the world.

One skilled in the art will recognize that the configuration shown inFIG. 2 would allow combining outputs of multiple such inverters into amulti-phase output.

FIG. 3 shows illustrative steady-state voltage and current waveforms forthe inverter and its associated controller shown in FIGS. 1 and 2. LowFCS frequency (6 kHz) is used for better waveform visibility.

FIG. 4 shows illustrative transient voltage and current waveforms forthe inverter and its associated controller shown in FIGS. 1 and 2. LowFCS frequency (6 kHz) is used for better waveform visibility.

In both FIG. 3 and FIG. 4, low FCS frequency (6 kHz) was used for betterwaveform visibility, and the switches were implemented using SiC powerMOSFETs.

FIG. 5 provides an illustrative schematic of a controller circuitimplementation.

One may see that this controller comprises an (inverting) integratorcharacterized by an integration time constant T, where the integratorinput comprises a sum of (1) the signal proportional to the switchingvoltage, μV*, (2) the reference AC voltage V_(ref), and (3) the signalproportional to the time derivative of the output AC voltage, μτ{dotover (V)}_(out).

The controller further comprises two comparators outputting the SCSs Q₁and Q₂.

A sum of the integrator output and the FCS V_(FCS) (which is a periodictriangle wave in his example) is supplied to the positive terminal ofthe comparator providing the output Q₁, and to the negative terminal ofthe comparator providing the output Q₂.

The reference thresholds for the comparators are provided by a resistivevoltage divider as shown in the figure, and the threshold value suppliedto the negative terminal of the comparator providing the output Q₂ isΔV_(FCS) larger than the threshold value supplied to the positiveterminal of the comparator providing the output Q₁.

To further illustrate the essential features of the asynchronous buckinverter of the present invention, and of its associated controller, letus consider a particular implementation example shown in FIG. 6.

Note that in this example the capacitance of the capacitor connected inparallel to the battery is only 10 μF. It would provide a relatively lowimpedance path for high-frequency current components. However, asignificantly larger capacitance (e.g., of order 1 mF, depending on thebattery's internal resistance) should be used to reduce the lowfrequency (e.g. twice the AC frequency) input current and voltageripples.

FIG. 7 shows simulated MOSFET and total power losses, efficiency, andtotal harmonic distortions as functions of the output power for theparticular inverter implementation shown in FIG. 6 (48 kHz FCS,resistive load).

FIG. 8 provides illustrative steady-state voltage and current waveformsfor a lagging PF=0.5 load (66.2 mH inductor in series with 14.4 Ωresistor), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 9 provides illustrative transient voltage and current waveforms fora lagging PF load (50 mH inductor in series with 10.8 Ω or 84.4 Ωresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 10 provides illustrative steady-state voltage and current waveformsfor a leading PF=0.5 load (106 μF capacitor in series with 14.4 Ωresistor), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 11 provides illustrative transient voltage and current waveformsfor a leading PF load (70.7 μF capacitor in series with 21.6 Ω or 1 MΩresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

2 Free-Running (Variable Frequency) Configuration of an Inverter of thePresent Invention

FIG. 12 shows an illustrative schematic of a particular implementationof a free-running version of the inverter and its associated controllershown in FIG. 1.

In a free-running configuration, the switching frequency varies with theoutput voltage, and its average value would depend on the input andoutput voltages and the load, and would be generally inverselyproportional to the value of the hysteresis gap of the Schmitt triggersand the time constant of the integrator.

With the components and the component values shown in FIG. 12, theinverter typically (e.g., in a steady state) operates in a discontinuousconduction mode (DCM) for the output powers ≲2.2 kW, and the modulationtype may be viewed as effectively a pulse-frequency modulation.

To illustrate the differences in switching behavior, FIG. 13 shows thepower spectra of the common (CM) and differential mode (DM) outputvoltages for the particular FCS-based (FIG. 6) and free-running (FIG.12) implementations. The vertical dashed lines are at 150 kHz.

3 Detailed Description of Basic Operation of an H-Bridge Inverter With aFree-Running ICM Controller

FIG. 14 shows a simplified schematic of a H-bridge inverter with afree-running ICM controller. As may be seen in the figure, the MOSFETswitches in the bridge are turned on or off by high or low values,respectively, of the switch control signals (SCS) Q₁ and Q₂ provided bythe controller, and the bridge outputs the switching voltage V*. Theswitching voltage is then filtered with a passive LC filtering networkto produce the output voltage V_(out). The ICM controller effectivelyconsists of (i) an integrator (with the time constant T) integrating asum of three inputs, and (ii) two Schmitt triggers with the samehysteresis gap Δh, inverting (out-putting Q₁) and non-inverting(outputting Q₂). A resistive divider ensures that the reference voltageof the non-inverting Schmitt trigger is slightly higher than that of theinverting one.

For the performance examples in this section that follow, the componentsand their nominal values are as follows:

The battery electromotive force (e.m.f.) is ε=450 V; the battery'sinternal resistance is 10 Ω; the capacitance of the capacitor connectedin parallel to the battery is 1,200 μF; the switches are the CreeC2M0025120D SiC MOSFETs; the diodes in parallel to the switches are theRohm SCS220KGC SiC Schottky diodes; the OpAmps are LT1211; thecomparators are LT1715; L=195 μH; C=4 μF; μ=1/200; R=10 kΩ; τ=47 μs(τ/R=4.7 nF); T=22 μs (T/R=2.2 nF); V_(s)=5 V; R′=10 kΩ; δR′=510 Ω;r=100 kΩ, and δr=10 kΩ.

Let us initially make a few sensible idealizations, including nearlyideal behavior of the controller circuit, insignificant voltage dropsacross the components of the bridge, negligible ohmic voltage dropsacross the reactive components, and approximately constant L and C. Wewould also assume a practical choice of T and Δh that would ensuresufficiently high switching frequencies for the switching ripples in theoutput voltage to be ignored, as they would be adequately filtered bythe LC circuit. This would imply that we may consider an instantaneousvalue of V_(out) within a switching cycle to be effectively equal to theaverage value of V_(out) over this cycle. With such idealizations, andprovided that |V_(ref)|<μ|V_(in)| at all times, the output voltageV_(out) may be expressed, in reference to FIG. 14, by the followingequation:

$\begin{matrix}{{{\overset{\_}{V}}_{out} = {\left( {{- \frac{{\overset{\_}{V}}_{ref}}{\mu}} - {2L{\overset{\overset{.}{\_}}{I}}_{load}}} \right) - {\tau\;{\overset{\overset{.}{\_}}{V}}_{out}} - {2{LC}\;{\overset{\overset{¨}{\_}}{V}}_{out}}}},} & (1)\end{matrix}$where I_(load) is the load current, the overdots denote timederivatives, μ is the nominal proportionality constant between thereference and the output voltages, and the overlines denote averagingover a time interval between a pair of rising or falling edges of eitherQ₁ or Q₂. Thus, according to equation (1), the output voltage of theinverter shown in FIG. 14 would be equal to the voltage −V _(ref)/μ−2Lİ_(load) filtered with a 2nd order lowpass filter with the undampednatural frequency ω_(n)=1/√{square root over (2LC)} and the qualityfactor Q=√{square root over (2LC)}/τ. The reference voltage V_(ref) inequation (1) may be an internal reference (e.g. for operating in anislanded mode), or an external reference (e.g. it may be proportional tothe mains voltage for synchronization with the grid).

3.1 Derivation of Equation (1)

Let us show how equation (1) may be derived by mapping the voltage andcurrent relations in the output LC filter to the voltage relations amongthe inputs and the output of the integrator in the ICM controller.

Indeed, for continuous function ƒ(t), the time derivative of its averageover a time interval ΔT may be expressed as

$\begin{matrix}{{{\overset{\overset{.}{\_}}{f}(t)} = {{\frac{d}{dt}\left\lbrack {\frac{1}{\Delta\; T}{\int_{t - {\Delta\; T}}^{t}{{dsf}(s)}}} \right\rbrack} = {\frac{1}{\Delta\; T}\left\lbrack {{f(t)} - {f\left( {t - {\Delta\; T}} \right)}} \right\rbrack}}},} & (2)\end{matrix}$and it will be zero if ƒ(t)−ƒ(t−ΔT)=0.

Note that rising and falling edges of an output of a Schmitt triggerhappen when its input crosses (effectively constant) respectivethresholds. Thus relating the inputs and the output of the integrator inthe ICM controller, differentiating both sides, then averaging between apair of rising or falling edges of either Q₁ or Q₂, would lead to

$\begin{matrix}{{\overset{\_}{V}}^{*} = {{- \frac{{\overset{\_}{V}}_{ref}}{\mu}} - {\tau\;{{\overset{\overset{.}{\_}}{V}}_{out}.}}}} & (3)\end{matrix}$On the other hand, from the voltage and current relations in the outputLC lifter,

$\begin{matrix}{{{\overset{\_}{V}}^{*} = {{\overset{\_}{V}}_{out} + {2L\;{\overset{\overset{.}{\_}}{I}}_{load}} + {2\;{LC}\;{\overset{\overset{¨}{\_}}{V}}_{out}}}},} & (4)\end{matrix}$and equating the right-hand sides of (3) and (4) would lead to equation(1).

3.2 Transient Responses

For convenience, we may define the “no-load ideal output voltage”V_(ideal) as

$\begin{matrix}{V_{ideal} = {{- \frac{V_{ref}}{\mu}} - {\tau\;{\overset{.}{V}}_{ideal}} - {2{LC}\;{{\overset{¨}{V}}_{ideal}.}}}} & (5)\end{matrix}$Then equation (1) may be rewritten as

$\begin{matrix}{{\overset{\_}{v} = {{{- \frac{2\mu\; L}{V_{0}}}{\overset{\overset{.}{\_}}{I}}_{load}} - {\tau\overset{\overset{.}{\_}}{v}} - {2{LC}\;\overset{\overset{¨}{\_}}{v}}}},} & (6)\end{matrix}$where v is a nondimensionalized error voltage that may be defined as thedifference between the actual and the ideal outputs in relation to themagnitude of the ideal output, for example, as

$\begin{matrix}{{v = \frac{V_{out} - V_{ideal}}{\max{V_{ideal}}}},} & (7)\end{matrix}$where max |V_(ideal)| is the amplitude of the ideal output. For asinusoidal reference V_(ref)=V₀sin(2#ƒ_(AC)t), and provided that Q≲1 andτƒ_(AC)<<<1, the no-load ideal output would be different from −V_(ref)/μby only a relatively small time delay and a negligible change in theamplitude. Then v may be expressed as v=μ(V_(out)−V_(ideal))/V₀.

Note that the symbol ≲ may be read as “smaller than or similar to”, andthe symbol <<< may be understood as “two orders or more smaller than”.

Thus, according to equation (6), the transients in the output voltage(in addition to the “normal” switching ripples at constant load) wouldbe proportional to the time derivative of the load current filtered witha 2nd order lowpass filter with the undamped natural frequencyω_(n)=1/√{square root over (2LC)} and the quality factor Q=√{square rootover (2LC)}/τ. Note that the magnitude of these transients would also beproportional to the output filter inductance L.

For example, for a step change at time t=t₀ in the conductance G of anohmic load, from G=G₁ to G=G₂, equation (6) would become

$\begin{matrix}{{\overset{\_}{v} = {{{- \frac{2\mu\;{{LV}_{out}\left( t_{0} \right)}}{V_{0}}}\left( {G_{2} - G_{1}} \right)\overset{\_}{\delta\left( {t - t_{0}} \right)}} - {\left\{ {\tau + {2{L\left\lbrack {{G_{1}\overset{\_}{\theta\left( {t_{0} - t} \right)}} + {G_{2}\overset{\_}{\theta\left( {t - t_{0}} \right)}}} \right\rbrack}}} \right\}\overset{\overset{.}{\_}}{v}} - {2{LC}\overset{\overset{¨}{\_}}{v}}}},} & (8)\end{matrix}$where θ(x) is the Heaviside unit step function [2] and δ(x) is the Diracδ-function [3]. In equation (8), the first term is the impulsedisturbance due to the step change in the load current, and V_(out)(t₀)is the output voltage at t=t₀. Note that δ(t−t₀) would be zero if t₀lies outside of the averaging interval ΔT, and would be equal to 1/ΔTotherwise.

Note that formally δ(t−t₀)=1/(2ΔT) when t₀ is exactly at the beginningor at the end of the averaging interval.

FIG. 15 provides an example of illustrative transient voltage andcurrent waveforms for a particular implementation of the inverter andits associated ICM controller shown in FIG. 14, in response tofull-range step changes in a resistive load. Note that the switchinginterval, as well as the inductor current and its operation mode (e.g.continuous (CCM) or discontinuous (DCM)) change according to the outputvoltage values and the load conditions, and would also change accordingto the power factor of the load.

It is also instructive to illustrate the robustness and stability ofthis inverter for other highly nonlinear loads. (A nonlinear electricalload is a load where the wave shape of the steady-state current does notfollow the wave shape of the applied voltage (i.e. impedance changeswith the applied voltage and Ohm's law is not applicable)). FIG. 16provides an example of voltage and current waveforms when the inverterwith its associated ICM controller shown in FIG. 14 is connected to afull-wave diode rectifier powering a 2 kW load.

FIG. 17 provides an example of transient voltage and current waveforms,for the same inverter, in response to connecting and disconnecting thereference voltage. This shows the “instantaneous” synchronization withreference, e.g., illustrating how the presented inverter may quicklydisconnect from and/or reconnect to the grid when used as a grid-tieinverter.

3.3 Switching Behavior and Efficiency Optimization

From the above mathematical description one may deduce that, for giveninductor and capacitor values, and for given controller parameters(e.g., T and Δh), the total switching interval (i.e., the time intervalbetween an adjacent pair of rising or falling edges of either Q₁ or Q₂),the duty cycle, and the “on” and “off” times, wound all vary dependingon the values and time variations V_(in), V_(ref), V_(out), and the loadcurrent. Thus the switching behavior of the ICM controller may not becharacterized in such simple terms as puke-width or pulse-frequencymodulation (PWM or PFM). This is illustrated in FIGS. 18 through 21,which show representative steady state waveforms at full (2 kW), and 10%(200 W) resistive loads.

In a steady state (i.e. for a constant load), the average value of theswitching interval would be generally proportional to the product of theintegrator time constant T and the hysteresis gap Δh of the Schmitttriggers (i.e. the values of r and δr). The particular value of theswitching interval would also depend on the absolute value of thereference voltage |V_(ref)| (as ∝ |V_(ref)|⁻¹), on the ratio|V_(ref)|/|V_(in)|, and on the load current [4, 5]. As a result, even ina steady state, for a sinusoidal AC reference the switching frequencywould span a continuous range of values, as illustrated in FIG. 22.which shows the power spectral density (PSD) of the inductor current atfull (2 kW) and 10% (200 W) resistive loads.

For given inverter components and their values, the power losses invarious components would be different nonlinear functions of the load,and would also exhibit different nonlinear dependences on the integratortime constant T and the hysteresis gap Δh. Thus, given a particularchoice of the MOSFET switches and their drivers, the magnetics, andother passive inverter components, by adjusting T and/or Δh one mayachieve the best overall compromise among various component power losses(e.g., between the bridge and the inductor losses), while remainingwithin other constraints on the inverter specifications.

FIG. 23 provides an example of simulated efficiency and total harmonicdistortion (THD) values as functions of the output power for aparticular inverter implementation using commercial off-the-shelf (COTS)components (including SiC MOSFETs and diodes), with the specificationsaccording to the technical requirements for the Little Box Challenge [6]outlined in [7]. In the efficiency simulations, high-fidelity modelswere used for the MOSFETs and diodes, and the inductor core and windinglosses were taken into account. The dashed line in the upper panel ofFIG. 23 plots the simulated efficiency with more conservative (doubled)estimated total losses, including the MOSFET and the inductor losses.

3.4 Startup Behavior

FIG. 24 illustrates the startup voltages (upper panel) and currents(lower panel) for a full (2 kW) resistive load connected to the outputof the inverter. As one may see, as long as the controller is poweredup, the battery may be connected to the input of the inverter (at 12.5ms in the figure), and the output voltage would quickly converge to thedesired output without excessive inrush currents and voltage transients.The only significant inrush current may be the initial current throughthe battery, charging the inverter's input capacitor during the timeinterval comparable with the product of the input capacitor and thebattery's internal resistance.

3.5 Improving Transient Response By Introducing Feedback of the LoadCurrent

One may infer from equation (1) that the term −2Lİ _(load) may becancelled by adding −2 μLİ_(load) to the input of the integrator.However, the switching ripples in the load current would normally makesuch an approach impractical. Instead, one should add a voltage2μLI_(load)/T directly to the inputs of the Schmitt triggers, asillustrated in FIG. 25.

Additionally, because of the propagation delays and other circuit,nonidealities, fast step current transients may not be cancelledexactly. Instead, the current feedback would try to “counteract” animpulse disturbance in the output voltage due to a step change in theload current by a closely following pulse of opposite polarity, mainlyreducing the frequency content of the transients that lies below theswitching frequencies. This is illustrated in FIG. 26, which comparesthe transient responses for an ICM controller without (left) and with(right) current feedback, when a leading PF=0.5 load is connected to anddisconnected from the output of the inverter with the frequency 1 kHzand 50% duty cycle. As indicated by the horizontal lines in the lowerpanels of the example of FIG. 26, the current feedback reduces the PSDof the transients at the load switching frequency (1 kHz) approximately12 dB.

4 Buck-Boost DC/DC Converter With ICM Controller

While above the ICM controller is disclosed in connection with a hardswitching H-bridge power inverter, the ICM concept may be extended, withproper modifications, to other hard- or soft-switching power inverterand DC /DC converter topologies.

As an illustration, FIG. 27 provides an example of a buck-boost DC/DCconverter with an ICM controller. When the feedback voltage V_(fb) isproportional to the output voltage, V_(fb)=−V_(out)/β, this converterwould provide an output voltage regulation with the nominal steady-stateoutput voltage βV_(ref). When the feedback voltage V_(fb) isproportional to the load current, V_(fb)=−RI*/β, this converter wouldprovide an output current regulation with the nominal steady-stateoutput current βV_(ref)/R. Note that in this example the load explicitlycontains a (parallel) capacitance that may be comparable with, or largerthan, the converter capacitance C, and thus the feedback voltage maycontain very strong high-frequency components. Further, when thefeedback voltage V_(fb) is proportional to the output power,V_(fb)=−V_(out)I*/I₀/β, this converter would provide an output powerregulation with the nominal steady-state output power βV_(ref)I₀.

FIG. 28 provides an example of transient waveforms for a particularimplementation of the converter shown in FIG. 27 configured for voltage,current, and power regulation.

For an isolated version, the converter inductor may be replaced by aflyback transformer, as indicated in the upper right corner of FIG. 27.

4.1 Startup Sequence for the Buck-Boost DC/DC Converter With ICMController

For a proper startup of the converter shown in FIG. 27, the initialvalue of the reference voltage V_(ref) should be zero. After both thecontroller circuit and the power stage are powered up, the referencevoltage should be ramped up from zero to the desired value over sometime interval. The duration of this time interval would depend on theconverter specifications and the component values, and would typicallybe in the 1 ms to 100 ms range.

For a particular implementation of the converter, FIG. 29 illustratesthe startup voltages and currents for a full resistive load connected tothe output of the converter (upper panel), and for no load at the output(lower panel). In this illustration, the controller circuit is poweredup first, with the reference voltage set to zero. At 5 ms, the batteryis connected to the converter input. At 10 ms, the reference voltagestarts ramping up from zero, reaching its desired value at 20 ms. As onemay see, with such a startup sequence there would be no excessively highinrush currents through the converter inductor.

5 ICM Control of 3-Phase Inverters

FIG. 30 provides an example of an ICM-controlled 3-phase inverter. Here,the output line-to-line voltages V_(ab), V_(bc), and V_(ca) would beproportional to the respective reference voltages V_(ab), V_(bc), andV_(ca), where V_(ab)+V_(bc)+V_(ca)=0. Note that, in general, thereference voltages do not need to be sinusoidal signals.

As one should be able to see in FIG. 30, the switches in the bridge arecontrolled by three instances of an ICM controller disclosed herein, andeach leg of the bridge is separately controlled by its respective ICMcontroller.

The switching voltages V*_(ab), V*_(bc), and V*_(ca) are the differencesbetween the voltages at nodes a, b, and c: V*_(ab)=V*_(a)−V*_(b),V*_(bc)=V*_(b)−V*_(c), and V*_(ca)=V*_(c)−V*_(a).

This inverter is characterized by the advantages shared with theH-bridge inverter presented above: robust, high quality, andwell-regulated AC output for a wide range of power factor loads,voltage-based control without the need for separate start-up management,the ability to power highly nonlinear loads, effectively instantaneoussynchronization with the reference (allowing to quickly disconnect fromand/or reconnect to the grid when used as a grid-tie inverter), andmultiple ways to optimize efficiency and thecost-size-weight-performance tradespace.

For example, FIG. 31 illustrates transient output voltages and currents,and the inductor currents, for a particular implementation of a 3 kWICM-controlled 3-phase inverter shown in FIG. 30, in response tofull-range (and independent of each other) step changes in theline-to-line resistive loads.

Note that for 3-phase loads that are not significantly unbalanced, thevalue of the input capacitor may be significantly reduced, in comparisonwith the single-phase H-bridge inverter, without exceeding the limits onthe input current ripples.

FIG. 32 illustrates the startup voltages and currents when the 3 kWICM-controlled 3-phase inverter shown in FIG. 30 is connected to a low(p.f.=0.1) lagging power factor load in Δ configuration, with theapparent power of about 3 kW. Note that the transient current throughthe battery is bi-directional, going through the discharge-rechargecycles as needed, before the steady-state operation is achieved.

6 Bidirectionality of ICM-Controlled Inverters and AC/DC Converters

FIG. 33 provides an example of a single-phase H-bridge ICM-based AC/DCconverter with high power factor and low harmonic distortions.

As before, let us make a few sensible idealizations, including nearlyideal behavior of the controller circuit, insignificant voltage dropsacross the components of the bridge, negligible ohmic voltage dropsacross the reactive components, and constant inductances L and theoutput capacitance C_(out). We also assume a practical choice of theintegrator time constant T in the ICM controller circuit, and thehysteresis gap Δh of the Schmitt triggers, that ensures sufficientlyhigh switching frequencies for the switching ripples in the outputvoltage to be ignored. This also implies that we can consider aninstantaneous value of V_(AC) within a switching cycle to be effectivelyequal to the average value of V_(AC) over this cycle.

Note that rising and falling edges of an output of a Schmitt triggerhappen when its input crosses (effectively constant) respectivethresholds. Thus relating the inputs and the output of the integrator inthe ICM controller in FIG. 33, differentiating both sides, thenaveraging between a pair of rising or falling edges of either Q₁ or Q₂,would lead toV*=V _(AC) −βτ{dot over (V)} _(AC).   (9)On the other hand, the line current I_(AC) in FIG. 33 may be related tothe line and switching voltages V_(AC) and V* according to the followingequation:

$\begin{matrix}{{{\overset{\_}{I}}_{A\; C} = {\frac{1}{2L}{\int{{dt}\left( {{\overset{\_}{V}}_{A\; C} - {\overset{\_}{V}}^{*}} \right)}}}},} & (10)\end{matrix}$and substituting V* from equation (9) into (10) would lead to

$\begin{matrix}{{{\overset{\_}{I}}_{A\; C} = {{\beta\frac{\tau}{2L}{\overset{\_}{V}}_{A\; C}} + {const}}},} & (11)\end{matrix}$where the constant of integration would be determined by the initialconditions and would decay to zero, due to the power dissipation in theconverter's components and the load, for a steady-state solution.

Thus in a steady state

${{\overset{\_}{I}}_{A\; C} = {{\beta\frac{\tau}{2\; L}{\overset{\_}{V}}_{A\; C}} \propto {\overset{\_}{V}}_{A\; C}}},$leading to AC/DC conversion with effectively unity power factor and lowharmonic distortions. Note that High power factor in the ICM-based AC/DCconverter shown in FIG. 33 is achieved without need for current sensing,and the PFC is entirely voltage-based.

The output parallel RC circuit forms a current filter which, withrespect to the input current fed by a current source, acts as a 1storder lowpass filter with the time constant τ_(out)=R_(load)C_(out), andthus, for sufficiently large τ_(out) (e.g. an order of magnitude largerthan ƒ_(AC) ⁻¹), the average value of the output voltage V_(out) wouldbe proportional to the RMS of the line voltage and may be expressed as

$\begin{matrix}{{\left\langle V_{out} \right\rangle = {{\left( {{\eta\beta}\; R_{load}\frac{\tau}{2L}} \right)^{\frac{1}{2}}\left\langle V_{A\; C}^{2} \right\rangle^{\frac{1}{2}}} = {K\left\langle V_{A\; C}^{2} \right\rangle^{\frac{1}{2}}}}},} & (12)\end{matrix}$where the angular brackets denote averaging over sufficiently large timeinterval (e.g. several AC cycles), η is the converter efficiency, andwhere (V_(AC) ²)^(½) is the RMS of the line voltage.

For example, for L=195 μH and τ=13.7 μs, 2L/τ≈28.5 Ω. Thus for β=1 and95% efficiency R_(load)=120 Ω would result in K≈2.

For regulation of the output voltage V_(out), the load conductance maybe obtained by sensing both the output voltage and the load currentI_(load), and the coefficient β may be adjusted and/or maintained to beproportional to the ratio I_(load)/V_(out).

For example, from equation (12),

$\begin{matrix}{\beta = {{\frac{2\; K^{2}L}{\eta\tau}R_{load}^{- 1}} = {\frac{2K^{2}L}{\eta\tau}\frac{I_{load}}{V_{out}}}}} & (13)\end{matrix}$would lead to the nominal AC/DC conversion ratio <V_(out)>)/(V_(AC)²>^(½)=K.

FIG. 34 illustrates the behavior of a particular implementation of a 2kW ICM-controlled single-phase AC/DC converter shown in FIG. 33. In thisexample, the load conductance switches (effectively instantaneously)between zero and the full load, and the coefficient β is obtainedaccording to equation (13). One should be able to see that, after theconverter is powered up (after the AC source is connected at t=2.75 ms),the output voltage converges to the value given equation (12), and theline current converges to the steady-state current given by equation(11) with const32 0. The bottom panel in FIG. 34 shows the PSD of thesteady-state current at full load, illustrating that the switchingfrequency would span a continuous range of values.

Further, additional output voltage regulation based on the differencebetween the desired nominal (“reference”) and the actual (<V_(out)>)output voltages may be added. For example, a term proportional to saiddifference may be added to the parameter β.

7 Variations of ICM Controller Topologies and 3-Phase AC/DC and DC/ACConverters

One skilled in the art will recognize that an ICM controller allowsmapping of the voltage relations among the inputs and the outputs of theintegrators in the ICM controller into various desired voltage andcurrent relations in a converter.

For example, as illustrated in FIG. 35(a), given a plurality ofintegrator inputs and a plurality of comparator (Schmitt trigger) inputsadded, along with the integrator output, to the comparator (Schmitttrigger) input, these pluralities of inputs may be related by thefollowing differential equation:

$\begin{matrix}{{{\frac{1}{T}{\sum\overset{\_}{\left( {{plurality}\mspace{14mu}{of}\mspace{14mu}{integrator}\mspace{14mu}{inputs}} \right)}}} = {\frac{d}{dt}{\sum\overset{\_}{\left( {{purality}\mspace{14mu}{of}\mspace{14mu}{added}\mspace{14mu}{comparator}\mspace{14mu}{inputs}} \right)}}}},} & (14)\end{matrix}$where the overlines denote averaging over a time interval between a pairof rising or falling edges of either first or second Schmitt trigger.Then (as illustrated, for example, in Sections 3.1 and 6) the desiredvoltage and current relations in a converter may be mapped (typically,through the relation to a switching voltage(s)) into the voltagerelations in an ICM controller.

Note that, in accordance with equation (14), the ICM controllers shownin FIGS. 35(b) and 35(c) would be effectively equivalent.

In FIG. 35(b) the integrator input signal comprises a first integratorinput component proportional to the switching voltage (μV*), a secondintegrator input component proportional to the AC source voltage(−μV_(AC)), and a third integrator input component proportional to atime derivative of said AC source voltage (βμτ{dot over (V)}_(AC)), andthe Schmitt trigger input signal comprises a first Schmitt trigger inputcomponent proportional to said integrator output signal and an optionalsecond Schmitt trigger input component proportional to a frequencycontrol signal (V_(FCS)).

In FIG. 35(c) the integrator input signal comprises a first integratorinput component proportional to the switching voltage (μV*) and a secondintegrator input component proportional to the AC source voltage(−μV_(AC)), and the Schmitt trigger input signal comprises a firstSchmitt trigger input component proportional to said integrator outputsignal, a second Schmitt trigger input component proportional to said ACsource voltage (βμτV_(AC)/T), and an optional third Schmitt triggerinput component proportional to a frequency control signal (V_(FCS)).

FIG. 36 provides an example of ICM-based control of a 3-phase AC/DCconverter with high power factor and low harmonic distortions. As oneshould be able to see in FIG. 36, the switches in the bridge arecontrolled by three instances of an ICM controller disclosed herein, andeach leg of the bridge is separately controlled by its respective ICMcontroller.

With β given by

$\begin{matrix}{{\beta = {\frac{K^{2}L}{3{\eta\tau}}\frac{I_{load}}{V_{out}}}},} & (15)\end{matrix}$where η is the converter efficiency, the nominal AC/DC conversion ratioof the 3-phase AC/DC converter shown in FIG. 36 would be<V_(out)>/<V_(LL) ²>^(½)=K, where V_(LL) is the nominal line-to-linevoltage. Further, additional output voltage regulation based on thedifference between the desired nominal (“reference”) and the actual(<V_(out)>) output voltages may be added. For example, a termproportional to said difference may be added to the parameter β.

Also, a desired voltage output V_(ref) may be achieved by using theparameter β that may be expressed as follows:

$\begin{matrix}{\beta = {\frac{3V_{ref}^{2}}{\left\langle V_{ab}^{2} \right\rangle\left\langle V_{bc}^{2} \right\rangle\left\langle V_{ca}^{2} \right\rangle}\frac{L}{\eta\tau}{\frac{I_{load}}{V_{out}}.}}} & (16)\end{matrix}$

Note that with the inputs to the integrators of the ICM controllers asshown in FIG. 36, any chosen single node of the power stage (e.g., V₊,V⁻, the “neutral” node V_(N), a switching node a, b, or c, or an AC nodeV_(a), V_(b), or V_(c)) may be grounded.

We may refer to the voltages V′_(a)=V_(a)−V_(N), V′_(b)=V_(b)−V_(N), andV′_(c)=V_(c)−V_(N) shown in FIG. 36 as line-to-neutral voltages of the3-phase source voltage. In practical implementations it would be commonthat the “neutral” node is grounded, i.e., V_(N)=0.

FIG. 37 illustrates the behavior of a particular implementation of a 6kW ICM-controlled 3-phase AC/DC converter shown in FIG. 36. In thisexample, the load conductance switches (effectively instantaneously)between 10% and the full load, and the coefficient β is obtainedaccording to equation (16).

Note that the ICM-based control of the converter shown in FIG. 36 wouldalso ensure that the difference between the common mode output voltageV_(CM)=(V₊+V⁻)/2 and the “neutral” node voltage V_(N) would be azero-mean voltage with the main frequency content at the switchingfrequencies. This is illustrated in panels (c) and (d) of FIG. 38, whichshow the PSDs of V_(CM)−V_(N) (with the “neutral” node grounded, i.e.,V_(N)==0) for the steady-state operation at full (panel (c)) and 10%(panel d)) of the nominal load for a particular implementation of a 6 kWICM-controlled 3-phase AC/DC, converter shown in FIG. 36.

Panels (a) and (b) of FIG. 38 show the PSDs of the steady-state inductorcurrents at full and 10% loads, illustrating low harmonic distortionsand the fact that the switching frequency would span a continuous rangeof values.

FIG. 39 provides an example of ICM-based control of a 3-phase AC/DCconverter that is effectively equivalent to that shown in FIG. 36. Inthis example, an input signal of the integrator in an ICM controller isa linear combination of voltages proportional to (1) a line-to-linevoltage (e.g. −μV_(ab)), (2) its time derivative (e.g. βμτ{dot over(V)}_(ab)), and (3) the difference between two respective switchingvoltages (e.g. μV*_(ab)).

FIG. 40 provides a example of an ICM-controlled 3-phase inverter (DC/ACconverter). Here, the output line-to-line voltages V_(ab)=V_(a)−V_(b),V_(bc)=V_(b)−V_(c), and V_(ca)=V_(c)−V_(a) would be proportional to therespective differences between the reference voltages V_(a)−V_(b),V_(b)−V_(c), and V_(c)−V_(a), where V_(a)+V_(b)+V_(c)=0. Note that, ingeneral, the reference voltages do not need to be sinusoidal signals.

We may refer to the voltages V′_(a)=V_(a)−V_(N), V′_(b)=V_(b)−V_(N), andV′_(c)=V_(c)−V_(N) shown in FIG. 40 as line-to-neutral voltages of the3-phase output voltage. Note that in practical implementations the“neutral” node V_(N) may be floating (not grounded), and thus may be a“virtual neutral”. Whether the node V_(N) is grounded or not, we mayrefer to it as the “virtual neutral”.

Further note that the virtual neutral is connected to the AC outputs bycapacitors, and that the capacitances of these capacitors may or may notbe effectively equal.

As one should be able to see in FIG. 40, the switches in the bridge arecontrolled by three instances of an ICM controller disclosed herein, andeach leg of the bridge is separately controlled by its respective ICMcontroller.

Note that with the inputs to the integrators of the ICM controllers asshown in FIG. 40, the ground may be placed at (connected to) any chosensingle node of the power stage (e.g., V₊, V⁻, the “neutral” node V_(N),a switching node a, b, or c, or an AC node V_(a), V_(b), or V_(c)).

Also note that the inputs signals of the integrator in an ICM controllerin the inverter shown in FIG. 40 may also be as shown in FIG. 30. InFIG. 30, an input signal of the integrator in an ICM controller is alinear combination of voltages proportional to (1) a difference betweentwo switching voltages (e.g. μV*_(ab)), (2) the time derivative of therespective line-to-line voltage (e.g. μτ{dot over (V)}_(ab)), and (3)the respective reference voltage (e.g. V_(ab)).

FIG. 41 illustrates transient output power, voltages and currents, andthe inductor currents, for a particular implementation of a 6kWICM-controlled 3-phase inverter shown in FIG. 40, in response tofull-range (and independent of each other) step changes in theline-to-line resistive loads.

REFERENCES

[1] Qing-Chang Zhong and T. Hornik. Control of Power Inverters inRenewable Energy and Smart Grid Integration. Wiley, 2013.

[2] R. Bracewell. The Fourier Transform and Its Applications, chapter“Heaviside's Unit Step Function, H(x)”, pages 61-65. McGraw-Hill, NewYork, 3rd edition. 2000.

[3] P. A. M. Dirac. The Principles of Quantum Mechanics. OxfordUniversity Press, London, 4th edition, 1958.

[4] A. V. Nikitin, “Method and apparatus for control of switched-modepower supplies.” U.S. Pat. No. 9,130,455 (8 Oct. 2015).

[5] A. V. Nikitin, “Switched-mode power supply controller.” U.S. Pat.No. 9,467,046 (11 Oct. 2016).

[6] “Little box challenge,” 26 Mar. 2016. [Online]. Available:http://en.wikipedia.org/ wiki/Little_Box_Challenge

[7] “Detailed inverter specifications, testing procedure, and technicalapproach and testing application requirements for the little boxchallenge,” 16 Jul. 2015. [Online]. Available:https://www.littleboxchallenge.com/pdf/LBC-InverterRequirements-20150717.pdf

Regarding the invention being thus described, it will be obvious thatthe same may be varied in many ways. Such variations are not to beregarded as a departure from the spirit and scope of the invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the claims. It is to beunderstood that while certain now preferred forms of this invention havebeen illustrated and described, it is not limited thereto except insofaras such limitations are included in the following claims.

I claim:
 1. A switching converter capable of converting a 3-phase ACsource voltage into a DC output voltage, wherein said 3-phase AC sourcevoltage is characterized by three AC line-to-neutral voltages, whereinan AC line-to-neutral voltage is one of said three AC line-to-neutralvoltages, wherein said DC output voltage is characterized by a DC commonmode voltage, wherein said switching converter comprises a 3-phasebridge comprising three pairs of switches and capable of providing threeswitching voltages, wherein a switching voltage is provided by a pair ofswitches controlled by a controller providing a 1st control signal and a2nd control signal, and wherein a 1st switch of said pair of switches iscontrolled by said 1st control signal and a 2nd switch of said pair ofswitches is controlled by said 2nd control signal, said switchingconverter further comprising: a) an integrator characterized by anintegration time constant and operable to receive an integrator inputsignal and to produce an integrator output signal, wherein saidintegrator output signal is proportional to an antiderivative of saidintegrator input signal; b) a 1st Schmitt trigger characterized by ahysteresis gap and a 1st reference level, and operable to receive aSchmitt trigger input signal and to output said 1st control signal; andc) a 2nd Schmitt trigger characterized by said hysteresis gap and a 2ndreference level, and operable to receive said Schmitt trigger inputsignal and to output said 2nd control signal; wherein said integratorinput signal comprises a 1st integrator input component proportional tothe difference between said switching voltage and said DC common modevoltage and a 2nd integrator input component proportional to said ACline-to-neutral voltage, and wherein said Schmitt trigger input signalcomprises a 1st Schmitt trigger input component proportional to saidintegrator output signal.
 2. The switching converter of claim 1 whereinsaid integrator input signal further comprises a 3rd integrator inputcomponent proportional to a time derivative of said AC line-to-neutralvoltage.
 3. The switching converter of claim 2 wherein said switchingconverter is characterized an AC/DC voltage conversion ratio and whereinthe magnitude of said 3rd integrator input component proportional to atime derivative of said AC line-to-neutral voltage is chosen to providesaid AC/DC voltage conversion ratio.
 4. The switching converter of claim2 wherein said DC output voltage is characterized by a desired DCvoltage value and wherein the magnitude of said 3rd integrator inputcomponent proportional to a tune derivative of said AC line-to-neutralvoltage is chosen. to provide said desired DC voltage value.
 5. Theswitching converter of claim 1 wherein said Schmitt trigger input signalfurther comprises a 2nd Schmitt trigger input component proportional tosaid AC line-to-neutral voltage.
 6. The switching converter of claim 5wherein said switching converter is characterized by an AC/DC voltageconversion ratio and wherein the magnitude of said 2nd Schmitt triggerinput component proportional to said AC line-to-neutral voltage ischosen to provide said AC/DC voltage conversion ratio.
 7. The switchingconverter of claim 5 wherein said DC output voltage is characterized bya desired DC voltage value and wherein the magnitude of said 2nd Schmitttrigger input component proportional to said AC line-to-neutral voltageis chosen to provide said desired DC voltage value.
 8. A switchingconverter capable of converting a DC source voltage into a 3-phase ACoutput voltage, wherein said 3-phase AC output voltage is characterizedby three AC line-to-line voltages indicative of respective AC referencevoltages, wherein an AC line-to-line voltage is one of said three ACline-to-line voltages, wherein said switching converter comprises a3-phase bridge comprising three pairs of switches and capable ofproviding three switching voltages, wherein a switching voltage isprovided by a pair of switches controlled by a controller providing a1st control signal and a 2nd control signal, and wherein a 1st switch ofsaid pair of switches is controlled by said 1st control signal and a 2ndswitch of said pair of switches is controlled by said 2nd controlsignal, said switching converter further comprising: a) an integratorcharacterized by an integration time constant and operable to receiveall integrator input signal and to produce an integrator output signal,wherein said integrator output signal is proportional to anantiderivative of said integrator input signal; b) a 1st Schmitt triggercharacterized by a hysteresis gap and a 1st reference level, andoperable to receive a Schmitt trigger input signal and to output said1st control signal; and c) a 2nd Schmitt trigger characterized by saidhysteresis gap and a 2nd reference level, and operable to receive saidSchmitt trigger input signal and to output said 2nd control signal;wherein said integrator input signal comprises a voltage proportional toa difference between two switching voltages and a voltage proportionalto the respective reference voltage, and wherein said Schmitt triggerinput signal comprises a 1st Schmitt trigger input componentproportional to said integrator output signal.
 9. The switchingconverter of claim 8 wherein said integrator input signal furthercomprises a voltage proportional to a time derivative of the respectiveline-to-line voltage.
 10. The switching converter of claim 8 whereinsaid Schmitt trigger input signal further comprises a 2nd Schmitttrigger input component proportional to the respective line-to-linevoltage.
 11. An AC/DC converter converting an AC source voltage into aDC output voltage, wherein said AC/DC converter comprises an H-bridgecapable of providing a switching voltage, and wherein said H bridgecomprises a 1st pair of switches controlled by a 1st control signal anda 2nd pair of switches controlled by a 2nd control signal, said AC/DCconverter further comprising: a) an integrator characterized by anintegration time constant and operable to receive an integrator inputsignal and to produce an integrator output signal, wherein saidintegrator output signal is proportional to an antiderivative of saidintegrator input signal; b) a 1st Schmitt trigger characterized by ahysteresis gap and a 1st reference level, and operable to receive aSchmitt trigger input signal and to output said 1st control signal; andc) a 2nd Schmitt trigger characterized by said hysteresis gap and a 2ndreference level, and operable to receive said Schmitt trigger inputsignal and to output said 2nd control signal; wherein said integratorinput signal comprises a voltage proportional to said switching voltageand a voltage proportional to said AC source voltage, and wherein saidSchmitt trigger input signal comprises a 1st Schmitt trigger inputcomponent proportional to said integrator output signal.
 12. The AC/DCconverter of claim 11 wherein said integrator input signal furthercomprises a voltage proportional to a time derivative of said AC sourcevoltage.
 13. The AC/DC converter of claim 12 wherein said converter ischaracterized by an AC/DC voltage conversion ratio and wherein themagnitude of said voltage proportional to a time derivative of said ACsource voltage is chosen to provide said AC/DC voltage conversion ratio.14. The AC/DC converter of claim 12 wherein said DC output voltage ischaracterized by a desired DC voltage value and wherein the magnitude ofsaid voltage proportional to a time derivative of said AC source voltageis chosen to provide said desired DC voltage value.
 15. The AC/DCconverter of claim 11 wherein said Schmitt trigger input signal furthercomprises a 2nd Schmitt trigger input component proportional to said ACsource voltage.
 16. The AC/DC converter of claim 15 wherein said AC/DCconverter is characterized by an AC/DC voltage conversion ratio andwherein the magnitude of said 2nd Schmitt trigger input componentproportional to said AC source voltage is chosen to provide said AC/DCvoltage conversion ratio.
 17. The AC/DC converter of claim 15 whereinsaid DC output voltage is characterized by a desired DC voltage valueand wherein the magnitude of said 2nd Schmitt trigger input componentproportional to said AC source voltage is chosen to provide said desiredDC voltage value.